New features

Quick Create and Quick View forms
Enhanced lookup controls, “+New” button
Business Rules: declarative UI, client-side actions
Guided Business Process Flows: Outcome-oriented, role-specific, can span multiple entities
Real-time (synchronous) workflows
Auto Save (30 second interval), can be disabled
Form notifications / messages
Mobile Client Application (MoCA): Windows 8, Android, iPhone
Tablets (Windows 8, iPad): Config/client-side code works in tablet, local data-caching
"Reimagined" UI (no pop-ups, streamlined navigation, touch-friendly, display images (1 per entity))
Editable grids for Product entry (Opps, Quotes, Orders and Invoices)
Bing maps
Exchange-CRM server-side synchronization
Yammer integration: contextual conversations
Initiate Lync and Skype actions from within CRM
Allow team access to individual records
Office 2013 compatibility
Azure integration
New "Customization Guide" (helps with implementation customizations in CRM 2013)
Field descriptions appear as an infotip (tooltip) in the CRM UI.
Social Insights, powered by InsideView
Composite Fields (e.g., a contact's first, middle and last name are shown together; address fields are combined into one field)
The Best Practices Analyzer (BPA) checks to see whether the configuration is in accordance with best practices.
Data encryption option (on-premises only)
MarketingPilot
Netbreeze
Skype

Updated / Enhanced features

To make more room for data, Microsoft removed the Ribbon (top) and Navigation Pane (left). Replaced with navigation drop-downs (top).
Work areas (Sales, Service, etc.) now appear by clicking CRM logo at top.
The "Jewel" in CRM 2011 is no longer displayed in 2013.
Command Bar replaces ribbon. Shows 5 commands with link to others.
Forms are white; Fields show "..." instead of rectangle field area
Microsoft no longer supports the CRM 4.0 means of creating the following: plug-ins, client-side scripting, custom workflow activities, "2007" web service endpoint, ISV folder for custom web applications
Can define business process flows (enhanced in 2013) for more entities.
CRM 2013 uses a single SQL Server table to store entity data. CRM setup (during an upgrade) merges the ExtensionBase data to the Base tables.
Fetch XML (FetchXml) has been expanded with a Left Outer Join option.